2. Camille launches a model rocket in an open field near her house. The rocket has a bit of a problem, being slightly off balance. Its trajectory is described by the function y = 60 ln(x + 1) – 6x for 0 sxs 36.15, where y is the rocket's height (in feet) above the ground, and x is the horizontal distance (in feet) between the launch site and a point directly below the rocket. Below is a graph of the trajectory of the rocket:

The position of a runner is given by s left parenthesis t right parenthesis equals 7 t squared metres from the starting point, t minutes after they begin to run. What is the runner's velocity at t = 5 minutes?

The area of a circle increases at a rate of 2 cm² /s. How fast is the radius changing when the radius is 5cm? a) Draw the picture. b) Write the given and unknown derivatives in d/dt notation. c) Label the variables. d) Proceed to solve and finish the problem. Reminder, keep solutions and answer in exact form and don't forget the units on the final answer.

a) A curve ha's equation y = x² cos x, x € R. E Evaluate the gradient of the curve at x = π. Give the answer in terms of . dy dx